球面中紧致子流形上Yang-Mills场的不稳定性和孤立性  

Instability and Isolation for Yang-Mills Fields over Compact Submanifold of Sphere

作　　者：蔡开仁[1] 徐慧群[1] 

机构地区：[1]杭州师范学院理学院,杭州310036

出　　处：《工程数学学报》2005年第5期898-902,共5页Chinese Journal of Engineering Mathematics

基　　金：浙江省自然科学基金.

摘　　要：设M是球面Sn+p中的n维紧致定向的浸入子流形,则存在一个仅与M的第二基本形式长度平方和平均曲率有关的正常数A,当n>4+A时,M上不存在非平凡的弱稳定的Yang-Mills场。从而推广了Simons的关于球面Sn是Yang-Mills不稳定的经典定理。本文也证明了球面的紧致子流形上的Yang-Mills场,存在空隙性现象。If M is an n-dimensional compact oriented submanifold immersed in a sphere S^n＋p, it is proved that, if n 〉 4 ＋ A ＋ 2σ where σ is the square length of the second fundamental form and A is a positive constant depending only on the square length of the second fundamental form and the mean curvature of M, there are no non-trivial weakly stable Yang-Mills fields on M. Thus we generalize a classical result due to Simons that the standard sphere S^n（n 〉 4） is Yang-Mills unstable. It is also shown that there is a gap phenomena for Yang-Mills fields on the compact submanifolds in the sphere.

关 键 词：YANG-MILLS场 子流形 不稳定性 孤立性 

分 类 号：O186[理学—数学]